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Calibration of Local Volatility Surfaces from Observed Market Call and Put Option Prices

Author

Listed:
  • Changwoo Yoo

    (Korea University
    Korea University)

  • Soobin Kwak

    (Korea University)

  • Youngjin Hwang

    (Korea University)

  • Hanbyeol Jang

    (Korea University)

  • Hyundong Kim

    (Gangneung-Wonju National University)

  • Junseok Kim

    (Korea University)

Abstract

We present a novel, straightforward, robust, and precise calibration algorithm for local volatility surfaces based on observed market call and put option prices. The proposed local volatility reconstruction method is based on the widely recognized generalized Black–Scholes partial differential equation, which is numerically solved using a finite difference scheme. In the proposed method, sample points are strategically placed in the underlying and time domains. The unknown local volatility function is represented using the scattered interpolant function. The primary contribution of this study is that our proposed algorithm not only optimizes the volatility values at the sample points but also optimizes the positions of the sample positions using a least squares method. This optimization process improves the accuracy and robustness of our calibration method. Furthermore, we do not use the Tikhonov regularization technique, which was frequently used to obtain smooth solutions. To validate the practical efficiency and superior performance of the proposed reconstruction method for local volatility functions, we conduct a series of computational experiments using real-world market option prices such as the KOSPI 200, S &P 500, Hang Seng, and Euro Stoxx 50 indices. The proposed algorithm offers financial market practitioners a reliable tool for calibrating local volatility surfaces using only market option prices, enabling more accurate pricing and risk management of financial derivatives.

Suggested Citation

  • Changwoo Yoo & Soobin Kwak & Youngjin Hwang & Hanbyeol Jang & Hyundong Kim & Junseok Kim, 2025. "Calibration of Local Volatility Surfaces from Observed Market Call and Put Option Prices," Computational Economics, Springer;Society for Computational Economics, vol. 65(3), pages 1147-1168, March.
    • Handle: RePEc:kap:compec:v:65:y:2025:i:3:d:10.1007_s10614-024-10590-9
    DOI: 10.1007/s10614-024-10590-9
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    References listed on IDEAS

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    1. Ferreiro-Ferreiro, Ana María & García-Rodríguez, José A. & Souto, Luis & Vázquez, Carlos, 2020. "A new calibration of the Heston Stochastic Local Volatility Model and its parallel implementation on GPUs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 467-486.
    2. Georgiev, Slavi G. & Vulkov, Lubin G., 2021. "Computation of the unknown volatility from integral option price observations in jump–diffusion models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 591-608.
    3. Chaeyoung Lee & Soobin Kwak & Youngjin Hwang & Junseok Kim, 2023. "Accurate and Efficient Finite Difference Method for the Black–Scholes Model with No Far-Field Boundary Conditions," Computational Economics, Springer;Society for Computational Economics, vol. 61(3), pages 1207-1224, March.
    4. Wang, Jian & Wen, Shuai & Yang, Mengdie & Shao, Wei, 2022. "Practical finite difference method for solving multi-dimensional black-Scholes model in fractal market," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    5. Kim, Sangkwon & Kim, Junseok, 2021. "Robust and accurate construction of the local volatility surface using the Black–Scholes equation," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    6. Yan, Dong & Lin, Sha & Hu, Zhihao & Yang, Ben-Zhang, 2022. "Pricing American options with stochastic volatility and small nonlinear price impact: A PDE approach," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
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